A connected dominating set (CDS) is commonly used to model a virtual backbone of a wireless network. To bound the distance that information must travel through the network, we explicitly restrict the diameter of a CDS to be no more than s leading to the concept of a dominating s-club. We prove...

Aiming to understand real-world hierarchical networks whose degree distributions are neither power law nor exponential, we construct a hybrid clique network that includes both homogeneous and inhomogeneous parts, and introduce an inhomogeneity parameter to tune the ratio between the homogeneous...

We study the structural properties of Russian stock market by means of analysis of the corresponding market graph. For this graph we found the distribution of correlations, edge density, maximum cliques and maximum independent sets. We also study the evolution of the structural properties of the...

Given a multinomial decomposable graphical model, we identify several alternative parametrizations; in particular we consider conditional probabilities of clique-residuals given separators, as well as generalized log-odds-ratios. For each such parametrization, we construct the corresponding...

In many practical important cases, a massive dataset can be represented as a very large network with certain attributes associated with its vertices and edges. Stock markets generate huge amounts of data, which can be use for constructing the network reflecting the market’s behavior. In this...

A wireless network solution is generally implemented when the bounds of walls of buildings and the constraints of wires need to be broken. Wireless technologies provide the potential for freedom of mobility which is undoubtedly a convenience for organisations in today’s market. The security of...